Cisplatin, carboplatin and oxaliplatin are platinum-based drugs that are widely used in cancer chemotherapy. Platinum–DNA adducts, which are formed following uptake of the drug into the nucleus of cells, activate several cellular processes that mediate the cytotoxicity of these platinum drugs. This review focuses on recently discovered cellular pathways that are activated in response to cisplatin, including those involved in regulating drug uptake, the signalling of DNA damage, cell-cycle checkpoints and arrest, DNA repair and cell death. Such knowledge of the cellular processing of cisplatin adducts with DNA provides valuable clues for the rational design of more efficient platinum-based drugs as well as the development of new therapeutic strategies.